On that bright fall morning, we strolled up... - Deepstash

On that bright fall morning, we strolled up Spring Street—a beautiful street lined with huge oak trees—and talked about fractions, though I wouldn’t have known to call them that. We were puzzling over—or, rather, I was puzzling over—how to fairly divide a pie (probably one of the Corner Confectionery’s apple pies). My dad, a mathematical physicist, a man with an active mind, but one of few words, was a gentle guide, letting me think through things on my own.

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A Big Question

Where do ideas come from? That’s a big question. Here’s a smaller one: Where do mathematical ideas come from? I’ve wondered about this from the time I first contemplated being a mathematician until long after I officially became one.

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The recipes for new ideas

How do Eureka moments happen? They do feel contingent & magical, arising in consciousness on their own. But looking at the history of breakthrough ideas there seem to be a rough 2-phase process: 

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It's that feeling of being untethered that gives the mind free rein to recombine the information from step 1 into something new. 

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Ideas come to us when we have a specific problem but we do not focus on solving the problem directly.

It’s not at all obvious how to go about thinking up some new twist on these things. A new idea can feel like a remarkable discovery

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Learning rate and limits to learning

Some people take longer to develop the relevant building-block insights to progress in deep subjects like math. The ability to acquire understanding may vary from person to person.

It is highly unlikely that less intelligent people have a limit to deep subjects. The obstacle to learning advanced mathematics is that it may take you longer than a very smart person.

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